A Mirror Descent Perspective of Smoothed Sign Descent

Recent work by Woodworth et al. (2020) shows that the optimization dynamics of gradient descent for overparameterized problems can be viewed as low-dimensional dual dynamics induced by a mirror map, explaining the implicit regularization phenomenon from the mirror descent perspective. However, the methodology does not apply to algorithms where update directions deviate from true gradients, such as ADAM. We use the mirror descent framework to study the dynamics of smoothed sign descent with a stability constant $\varepsilon$ for regression problems. We propose a mirror map that establishes equivalence to dual dynamics under some assumptions. By studying dual dynamics, we characterize the convergent solution as an approximate KKT point of minimizing a Bregman divergence style function, and show the benefit of tuning the stability constant $\varepsilon$ to reduce the KKT error.

HalluAudio: Hallucinating Frequency as Concepts for Few-Shot Audio Classification

Few-shot audio classification is an emerging topic that attracts more and more attention from the research community. Most existing work ignores the specificity of the form of the audio spectrogram and focuses largely on the embedding space borrowed from image tasks, while in this work, we aim to take advantage of this special audio format and propose a new method by hallucinating high-frequency and low-frequency parts as structured concepts. Extensive experiments on ESC-50 and our curated balanced Kaggle18 dataset show the proposed method outperforms the baseline by a notable margin. The way that our method hallucinates high-frequency and low-frequency parts also enables its interpretability and opens up new potentials for the few-shot audio classification.